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In a semicircle, a square is drawn with its diagonal perpendicular to the diameter. It is 1 unit away from the center and 4 units away from the circumference. What is the area of the orange square?

 

 Jul 5, 2021
 #1
avatar+121048 
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The  radius of  the  circle  must =  5  since  the  diagonal  is 1 unit from  the  center  and  4 units  from  the   circumference

 

Using  the Pythagorean Theorem.....the  length of  the  diagonal  =   sqrt ( 5^2  - 1)^2   =  sqrt (24)  

 

The  side of  the  square =   sqrt (24)   /sqrt (2)    = sqrt  12

 

The area of the  square =    (sqrt (12))^2   =   12

 

 

cool cool cool

 Jul 5, 2021

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